LITMIR.BIZ

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image’s coordinate system are described by the Jacobian matrix formed from the partial spatial derivatives of the B₀ field. If the magnet’s B₀ field map is known, the Jacobian is fully known and, in principle, can be used to correct the distortions. But no spatial encoding occurs in locations where the magnet’s static gradient is equal and opposite to the applied gradient, and the correction problem is singular. Because of this, it can be desirable to acquire the image twice, for example once with a positive readout gradient and once with the readout gradient current reversed to ensure that all locations are spatially encoded for at least one acquisition. A general approach is to use a “model-based reconstruction” where the “forward model” describes how measured data are produced given any object input to the model. Conversely, given a set of measured data, an inversion of the forward model (generally by some form of iterative search) finds the object giving the “best fit” to the data, possibly subject to some constraints or prior knowledge [125–128].

Acquisition approaches to the magnet inhomogeneity problem include relying on multiple spin echo sequences, which have a long history of use in the oil well-logging industry where NMR is performed in very inhomogeneous fields [129]. This approach was used with phase encoding and the fixed “readout” gradient inherent to an inhomogeneous magnet to image in single-sided devices [49,130] and in a Halbach cylinder with a built-in readout gradient [20,22]. Other approaches include quadratic phase-encoding approaches [131,132] and missing point steady-state free precession (MS-SSFP) methods [133].

      3.5.2.2 Limited Frequency Bandwidth of Tuned Radiofrequency Coils

      If the magnet is inhomogeneous, or has a built-in encoding field, the MR linewidth across the body will be larger than seen in canonical high-field scanners, which typically achieve proton linewidths of a few tens of Hertz over the brain. In addition to the encoding and reconstruction problems described earlier, the Q of the radiofrequency coil is often high enough so that the bandwidth (BW) of the coil is lower than that of the signal, diminishing detection in regions with high-frequency offsets.

On excitation, this could be compensated in the design of the radiofrequency pulse using knowledge of the coil’s response to counteract the effect at the frequencies at the edge of the coil’s response. Alternatively, one could simply damp the resonator with an external resistor switched in during transmit (at the expense of requiring increased radiofrequency power) [134]. But during reception, the high-Q coil will simply be inefficient at detecting spins in locations where the spin frequency exceeds the coil BW. The ability to receive across the full-imaging BW is critical, and becomes more difficult at low field. Low loss reception is important for maintaining the sensitivity of detection, so there is strong motivation to maximize Q by increasing L and reducing resistive losses in the coil. Furthermore, reduced radiofrequency losses in the tissue help keep the Q of head resonators in the 50–200 range across a wide variety of low- to mid-field strengths, since the coil BW (full width at half maximum of coil response) relates to Q through BW = v₀/Q (where v₀ is the Larmor frequency). As Q does not change much, in general the detection BW decreases at lower field. Assuming Q = 100 and an 80-mT magnet (v₀ = 3.4 MHz), the expected BW of the coil is 34 kHz (compared with a 640-kHz BW for a Q = 100 coil at 1.5 T). Even for homogeneous magnets, a typical readout gradient of 10 mT/m will introduce a proton linewidth of 84 kHz over the 20-cm head. Thus, a receive coil constructed with desirable high-Q properties will introduce substantial shading across the FOV.

Increasing the receive coil Q with resistors is a poor strategy from the signal-to-noise ratio point of view since this introduces losses and thus radiofrequency noise. Lossless methods are needed to alter the frequency response of the tuned circuit. The Fano–Bode BW theory describes a general limit for the BW over which the impedance match of an MR coil can be achieved [135]. Cryoprobes at high field experience a similar issue [136]. In addition to traditional impedance matching methods, lossless manipulation of the tuned circuit frequency response can be addressed using a variant of preamplifier decoupling, typically used to reduce geometric coupling in arrays [137]. Traditional preamplifier decoupling uses a non-power-matched input impedance preamplifier to couple an extra parallel LC “trap” circuit to coil resonance. The lack of a power match is immaterial if the noise performance of the preamplifier is satisfactory with that matching condition. Because a power match is not used, it’s not clear if the Fano–Bode theory applies. Although known for causing a large perturbation to the coil’s frequency response, preamp decoupling at modest levels can create a minor split-resonance, which has the effect of lossless broadening the response. Figure 3.8 shows the frequency response of a low-impedance preamplifier (WanTcom Inc., Chanhassen, MN) connected to a coil tuned to 3.4 MHz. The strategy is able to reduce the coil’s power response variation over the desired imaging BW (shaded region of Figure 3.8) from 4.7 dB to 0.7 dB.

Figure 3.8 Response of a low-field magnetic resonance imaging coil with and without preamplifier decoupling. With mild preamplifier decoupling, the variation over the expected imaging bandwidth dropped from 4.7 dB to 0.7 dB.

      3.5.2.3 External EMI Removal (Eliminating the Shielded Room)

      Typical MRI scanners are sited inside a passively shielded conductive room (Faraday cage) to prevent external radiofrequency sources from inducing image artifacts. This >US$100 000 siting component is both costly and prevents portability. Passive shielding can be partially achieved by placing copper foil around the magnet. The passive radiofrequency shielding is generally sufficient for phantoms and objects that do not extend outside of the magnet (shielded area) but proves insufficient when a human subject is in the magnet. This is because the conductive human torso and legs act as an antenna which picks up external radiofrequency interference and pipes it into the detection coil. Imaging a cantaloupe and a living human can differ in external interference artifact by as much as 100-fold.

Additional EMI mitigation can be achieved using external interference detectors (additional radiofrequency coils outside of the magnet) and retrospective removal from the images. The interference is picked up from external coils and the artifact is removed from the image using a trained correlation model between that seen in imaging coil and the external detection coil. This approach has a broad history in electromagnetic measurements and in EEG and magnetoencephalography (MEG). Muller-Petke provides some review as well as an application to MR [138], and several methods have emerged specifically for low-field MRI systems [139,140]. Figure 3.9 shows results of an example phantom experiment in an 80-mT portable brain scanner [20,141] using retrospective EMI correction with five external detector coils [140]. Although refinements will continue, it appears that the EMI issue can be managed for POC MRI without a Faraday-shielded room.

Figure 3.9 Retrospective EMI correction of a time-varying EMI using five external coils using a k-space correlation matrix approach in a low-field scanner [140]. Four electromagnetic interference (EMI) sources are shown including a dynamic source (right-hand column). The bottom row shows difference images using “Ground Truth” (GT) images obtained without the noise sources present.

      3.6 Conclusions

      Research in MRI technology has done a phenomenal job of expanding diagnostic benefit by developing acquisition techniques and instrumentation to enable MRI scanners to “see more” through improved sensitivity, spatio-temporal resolution, contrasts, and expanded clinical targets. In contrast to the clear benefits achieved in this direction, extending the reach of MRI by widening the range of where it can be applied has received less attention (until recently). This is especially seen for MRI technology designed to extend its use at the POC such as emergency medicine settings by reducing

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